How to separate the object to smaller units to give different materials to the different parts?
Materials are assigned on a per-face basis. You can think of assignment to an object as a convenience function: 'Assign to all faces in the object's mesh'.
Assign to individual faces in Edit Mode. Add slots using the '+' sign next to the material slots panel. Select or create materials to occupy the slots.

Select the slot. Select the faces. Hit 'Assign'.